%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC204-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:40:23 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 31
% Syntax : Number of formulae : 104 ( 15 unt; 16 def)
% Number of atoms : 282 ( 60 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 319 ( 141 ~; 162 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 17 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 35 ( 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f74,axiom,
! [U] :
( app(nil,U) = U
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f75,axiom,
! [U] :
( nil = U
| ssList(tl(U))
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f76,axiom,
! [U] :
( nil = U
| ssItem(hd(U))
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f85,axiom,
! [U,V] :
( ssList(app(V,U))
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f99,axiom,
! [U,V] :
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f100,axiom,
! [U,V] :
( V = U
| neq(V,U)
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f104,axiom,
! [U] :
( nil = U
| cons(hd(U),tl(U)) = U
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f188,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f189,negated_conjecture,
ssList(sk4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f190,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f191,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f192,negated_conjecture,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
! [A,B] :
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| app(sk3,B) != A
| tl(sk4) != B
| ~ ssList(B)
| sk4 = A
| ~ ssList(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
( ~ neq(sk4,nil)
| ~ neq(sk1,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f205,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f272,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f273,plain,
! [X0] :
( nil = X0
| ssList(tl(X0))
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f274,plain,
! [X0] :
( nil = X0
| ssItem(hd(X0))
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f283,plain,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f298,plain,
! [V] :
( ~ ssList(V)
| ! [U] :
( ~ ssItem(U)
| cons(U,V) != V ) ),
inference(miniscoping,[status(thm)],[f99]) ).
fof(f299,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != X1 ),
inference(cnf_transformation,[status(thm)],[f298]) ).
fof(f300,plain,
! [X0,X1] :
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f304,plain,
! [X0] :
( nil = X0
| cons(hd(X0),tl(X0)) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f430,plain,
ssList(sk3),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f431,plain,
ssList(sk4),
inference(cnf_transformation,[status(thm)],[f189]) ).
fof(f432,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f433,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f434,plain,
( neq(sk2,nil)
| neq(sk2,nil) ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f439,plain,
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| ! [A,B] :
( app(sk3,B) != A
| tl(sk4) != B
| ~ ssList(B)
| sk4 = A
| ~ ssList(A) ) ),
inference(miniscoping,[status(thm)],[f196]) ).
fof(f440,plain,
! [X0,X1] :
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| app(sk3,X1) != X0
| tl(sk4) != X1
| ~ ssList(X1)
| sk4 = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f439]) ).
fof(f441,plain,
( ~ neq(sk4,nil)
| ~ neq(sk1,nil) ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f449,definition,
( sQ2_spl
<=> neq(sk2,nil) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f450,plain,
( ~ sQ2_spl
| neq(sk2,nil) ),
inference(component_clause,[status(thm)],[f449]) ).
fof(f452,plain,
sQ2_spl,
inference(split_clause,[status(thm)],[f434,f449]) ).
fof(f453,definition,
( sQ3_spl
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f455,plain,
( sQ3_spl
| ~ neq(sk4,nil) ),
inference(component_clause,[status(thm)],[f453]) ).
fof(f457,definition,
! [X0,X1] :
( sQ4_spl
<=> ( app(sk3,X1) != X0
| tl(sk4) != X1
| ~ ssList(X1)
| sk4 = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f458,plain,
! [X0,X1] :
( ~ sQ4_spl
| app(sk3,X1) != X0
| tl(sk4) != X1
| ~ ssList(X1)
| sk4 = X0
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f457]) ).
fof(f460,definition,
( sQ5_spl
<=> neq(nil,sk4) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f462,plain,
( sQ5_spl
| ~ neq(nil,sk4) ),
inference(component_clause,[status(thm)],[f460]) ).
fof(f464,definition,
( sQ6_spl
<=> neq(sk1,nil) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f466,plain,
( sQ6_spl
| ~ neq(sk1,nil) ),
inference(component_clause,[status(thm)],[f464]) ).
fof(f468,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f440,f457,f460,f453]) ).
fof(f469,plain,
( ~ sQ3_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f441,f464,f453]) ).
fof(f501,plain,
( ~ sQ2_spl
| neq(sk4,nil) ),
inference(forward_demodulation,[status(thm)],[f432,f450]) ).
fof(f502,plain,
( sQ6_spl
| ~ neq(sk3,nil) ),
inference(forward_demodulation,[status(thm)],[f433,f466]) ).
fof(f503,plain,
( sQ3_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f455,f501]) ).
fof(f504,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f503]) ).
fof(f505,plain,
( ~ sQ4_spl
| ~ ssList(tl(sk4))
| sk4 = app(sk3,tl(sk4))
| ~ ssList(app(sk3,tl(sk4))) ),
inference(destructive_equality_resolution,[status(thm)],[f458]) ).
fof(f506,plain,
( ~ sQ4_spl
| ~ ssList(sk3)
| ~ ssList(tl(sk4))
| ~ ssList(tl(sk4))
| sk4 = app(sk3,tl(sk4)) ),
inference(resolution,[status(thm)],[f505,f283]) ).
fof(f507,definition,
( sQ7_spl
<=> sk4 = app(sk3,tl(sk4)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f508,plain,
( ~ sQ7_spl
| sk4 = app(sk3,tl(sk4)) ),
inference(component_clause,[status(thm)],[f507]) ).
fof(f510,definition,
( sQ8_spl
<=> ssList(tl(sk4)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f512,plain,
( sQ8_spl
| ~ ssList(tl(sk4)) ),
inference(component_clause,[status(thm)],[f510]) ).
fof(f513,definition,
( sQ9_spl
<=> ssList(sk3) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f515,plain,
( sQ9_spl
| ~ ssList(sk3) ),
inference(component_clause,[status(thm)],[f513]) ).
fof(f516,plain,
( ~ sQ4_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f506,f507,f510,f513,f457]) ).
fof(f517,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f515,f430]) ).
fof(f518,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f517]) ).
fof(f519,plain,
( sQ8_spl
| nil = sk4
| ~ ssList(sk4) ),
inference(resolution,[status(thm)],[f512,f273]) ).
fof(f520,definition,
( sQ10_spl
<=> ssList(sk4) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f522,plain,
( sQ10_spl
| ~ ssList(sk4) ),
inference(component_clause,[status(thm)],[f520]) ).
fof(f523,definition,
( sQ11_spl
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f524,plain,
( ~ sQ11_spl
| nil = sk4 ),
inference(component_clause,[status(thm)],[f523]) ).
fof(f526,plain,
( sQ8_spl
| sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f519,f520,f523,f510]) ).
fof(f527,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f522,f431]) ).
fof(f528,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f527]) ).
fof(f556,plain,
( sQ5_spl
| nil = sk4
| ~ ssList(nil)
| ~ ssList(sk4) ),
inference(resolution,[status(thm)],[f462,f300]) ).
fof(f564,definition,
( sQ15_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f566,plain,
( sQ15_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f564]) ).
fof(f567,plain,
( sQ5_spl
| sQ11_spl
| ~ sQ15_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f556,f520,f564,f523,f460]) ).
fof(f568,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f566,f205]) ).
fof(f569,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f568]) ).
fof(f579,plain,
( sQ6_spl
| ~ sQ11_spl
| ~ neq(sk3,sk4) ),
inference(forward_demodulation,[status(thm)],[f524,f502]) ).
fof(f581,plain,
( sQ6_spl
| ~ sQ11_spl
| sk3 = sk4
| ~ ssList(sk3)
| ~ ssList(sk4) ),
inference(resolution,[status(thm)],[f579,f300]) ).
fof(f585,definition,
( sQ17_spl
<=> sk3 = sk4 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f586,plain,
( ~ sQ17_spl
| sk3 = sk4 ),
inference(component_clause,[status(thm)],[f585]) ).
fof(f589,plain,
( sQ6_spl
| ~ sQ11_spl
| sQ17_spl
| ~ sQ9_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f581,f520,f513,f585,f523,f464]) ).
fof(f592,plain,
( sQ6_spl
| ~ sQ17_spl
| ~ neq(sk4,nil) ),
inference(forward_demodulation,[status(thm)],[f586,f502]) ).
fof(f593,plain,
( sQ6_spl
| ~ sQ17_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f592,f501]) ).
fof(f594,plain,
( sQ6_spl
| ~ sQ17_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f593]) ).
fof(f596,plain,
( sQ6_spl
| sk3 = nil
| ~ ssList(sk3)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f502,f300]) ).
fof(f597,definition,
( sQ18_spl
<=> sk3 = nil ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f598,plain,
( ~ sQ18_spl
| sk3 = nil ),
inference(component_clause,[status(thm)],[f597]) ).
fof(f601,plain,
( sQ6_spl
| sQ18_spl
| ~ sQ9_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f596,f564,f513,f597,f464]) ).
fof(f613,plain,
! [X0] :
( ~ sQ18_spl
| sk3 = X0
| cons(hd(X0),tl(X0)) = X0
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f598,f304]) ).
fof(f625,plain,
! [X0] :
( ~ sQ18_spl
| app(sk3,X0) = X0
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f598,f272]) ).
fof(f627,plain,
( ~ sQ7_spl
| ~ sQ18_spl
| sk4 = tl(sk4)
| ~ ssList(tl(sk4)) ),
inference(paramodulation,[status(thm)],[f508,f625]) ).
fof(f629,definition,
( sQ20_spl
<=> sk4 = tl(sk4) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f630,plain,
( ~ sQ20_spl
| sk4 = tl(sk4) ),
inference(component_clause,[status(thm)],[f629]) ).
fof(f632,plain,
( ~ sQ7_spl
| ~ sQ18_spl
| sQ20_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f627,f510,f629,f597,f507]) ).
fof(f663,plain,
( ~ sQ20_spl
| ~ sQ18_spl
| sk3 = sk4
| cons(hd(sk4),sk4) = sk4
| ~ ssList(sk4) ),
inference(paramodulation,[status(thm)],[f630,f613]) ).
fof(f664,definition,
( sQ23_spl
<=> cons(hd(sk4),sk4) = sk4 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f665,plain,
( ~ sQ23_spl
| cons(hd(sk4),sk4) = sk4 ),
inference(component_clause,[status(thm)],[f664]) ).
fof(f667,plain,
( ~ sQ20_spl
| ~ sQ18_spl
| sQ17_spl
| sQ23_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f663,f520,f664,f585,f597,f629]) ).
fof(f669,definition,
( sQ24_spl
<=> ssItem(hd(sk4)) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f671,plain,
( sQ24_spl
| ~ ssItem(hd(sk4)) ),
inference(component_clause,[status(thm)],[f669]) ).
fof(f901,plain,
! [X0] :
( ~ sQ18_spl
| sk3 = X0
| ssItem(hd(X0))
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f598,f274]) ).
fof(f930,plain,
( ~ sQ23_spl
| ~ ssList(sk4)
| ~ ssItem(hd(sk4)) ),
inference(resolution,[status(thm)],[f299,f665]) ).
fof(f932,plain,
( ~ sQ23_spl
| ~ sQ10_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f930,f669,f520,f664]) ).
fof(f934,plain,
( ~ sQ18_spl
| sQ24_spl
| sk3 = sk4
| ~ ssList(sk4) ),
inference(resolution,[status(thm)],[f671,f901]) ).
fof(f935,plain,
( ~ sQ18_spl
| sQ24_spl
| sQ17_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f934,f520,f585,f669,f597]) ).
fof(f936,plain,
$false,
inference(sat_refutation,[status(thm)],[f452,f468,f469,f504,f516,f518,f526,f528,f567,f569,f589,f594,f601,f632,f667,f932,f935]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC204-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n017.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 08:00:26 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.070413 seconds
% 0.13/0.43 % CPU time: 0.252480 seconds
% 0.13/0.43 % Total memory used: 111.576 MB
% 0.13/0.43 % Net memory used: 111.343 MB
%------------------------------------------------------------------------------